Proceedings of the American Mathematical Society, Series B最新文献

{"title":"On a refinement of the non-orientable 4-genus of Torus knots","authors":"J. Sabloff","doi":"10.1090/bproc/166","DOIUrl":"https://doi.org/10.1090/bproc/166","url":null,"abstract":"In formulating a non-orientable analogue of the Milnor Conjecture on the \u0000\u0000 \u0000 4\u0000 4\u0000 \u0000\u0000-genus of torus knots, Batson [Math. Res. Lett. 21 (2014), pp. 423–436] developed an elegant construction that produces a smooth non-orientable spanning surface in \u0000\u0000 \u0000 \u0000 B\u0000 4\u0000 \u0000 B^4\u0000 \u0000\u0000 for a given torus knot in \u0000\u0000 \u0000 \u0000 S\u0000 3\u0000 \u0000 S^3\u0000 \u0000\u0000. While Lobb [Math. Res. Lett. 26 (2019), pp. 1789] showed that Batson’s surfaces do not always minimize the non-orientable \u0000\u0000 \u0000 4\u0000 4\u0000 \u0000\u0000-genus, we prove that they do minimize among surfaces that share their normal Euler number. We also determine the possible pairs of normal Euler number and first Betti number for non-orientable surfaces whose boundary lies in a class of torus knots for which Batson’s surfaces are non-orientable \u0000\u0000 \u0000 4\u0000 4\u0000 \u0000\u0000-genus minimizers.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125499801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vanishing cycle control by the lowest degree stalk cohomology","authors":"D. Massey","doi":"10.1090/bproc/93","DOIUrl":"https://doi.org/10.1090/bproc/93","url":null,"abstract":"Given the germ of an analytic function on affine space with a smooth critical locus, we prove that the constancy of the reduced cohomology of the Milnor fiber in lowest possible non-trivial degree off a codimension two subset of the critical locus implies that the vanishing cycles are concentrated in lowest degree and are constant.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127583266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonexistence and parameter range estimates for convolution differential equations","authors":"C. Goodrich","doi":"10.1090/bproc/130","DOIUrl":"https://doi.org/10.1090/bproc/130","url":null,"abstract":"<p>We consider nonlocal differential equations with convolution coefficients of the form <disp-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"minus upper M left-parenthesis left-parenthesis a asterisk u Superscript q Baseline right-parenthesis left-parenthesis 1 right-parenthesis right-parenthesis u left-parenthesis t right-parenthesis equals lamda f left-parenthesis t comma u left-parenthesis t right-parenthesis right-parenthesis comma t element-of left-parenthesis 0 comma 1 right-parenthesis comma\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>a</mml:mi>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mi>q</mml:mi>\u0000 </mml:msup>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>λ<!-- λ --></mml:mi>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">begin{equation} -MBig (big (a*u^qbig )(1)Big )u(t)=lambda fbig (t,u(t)big ),tin (0,1),notag end{equation}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</disp-formula>\u0000 and we demonstrate an explicit range of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xml","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115051978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The stability threshold and Diophantine approximation","authors":"Y. He, M. Ru","doi":"10.1090/bproc/64","DOIUrl":"https://doi.org/10.1090/bproc/64","url":null,"abstract":"The purpose of this paper is to use the filtration that appeared in Ru and Vojta [Amer. J. Math. 142 (2020), pp. 957-991] to extend the result of Blum-Jonsson [Adv. Math. 365 (2020), p. 57], as well as to explore some connections between the notion of the \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-stability and Diophantine approximation, especially the \u0000\u0000 \u0000 β\u0000 beta\u0000 \u0000\u0000-constant and the Ru-Vojta’s theorem.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115177855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A quadruple integral involving the product of generalized parabolic cylinder functions 𝐷ᵥ(𝛽𝑥)𝐷ᵤ(𝛼𝑧): Derivation and evaluation","authors":"Robert Reynolds, Allan Stauffer","doi":"10.1090/bproc/126","DOIUrl":"https://doi.org/10.1090/bproc/126","url":null,"abstract":"<p>The aim of the present document is to evaluate a quadruple integral involving the product of the generalized Parabolic Cylinder functions <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D Subscript v Baseline left-parenthesis beta x right-parenthesis upper D Subscript u Baseline left-parenthesis alpha z right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>D</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>v</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>β<!-- β --></mml:mi>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>D</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>u</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mi>z</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">D_{v}(beta x)D_{u}(alpha z)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> expressed in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124590471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topological obstructions to the diagonalisation of pseudodifferential systems","authors":"Matteo Capoferri, G. Rozenblum, N. Saveliev, D. Vassiliev","doi":"10.1090/bproc/147","DOIUrl":"https://doi.org/10.1090/bproc/147","url":null,"abstract":"Given a matrix pseudodifferential operator on a smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127689390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conformal images of Carleson curves","authors":"C. Bishop","doi":"10.1090/bproc/69","DOIUrl":"https://doi.org/10.1090/bproc/69","url":null,"abstract":"<p>We show that if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma\">\u0000 <mml:semantics>\u0000 <mml:mi>γ<!-- γ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">gamma</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a curve in the unit disk, then arclength on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma\">\u0000 <mml:semantics>\u0000 <mml:mi>γ<!-- γ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">gamma</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a Carleson measure iff the image of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma\">\u0000 <mml:semantics>\u0000 <mml:mi>γ<!-- γ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">gamma</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> has finite length under every conformal map of the disk onto a bounded domain with a rectifiable boundary.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133950700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons","authors":"Xu Cheng, E. Ribeiro, Detang Zhou","doi":"10.1090/bproc/155","DOIUrl":"https://doi.org/10.1090/bproc/155","url":null,"abstract":"In this article, we investigate the geometry of \u0000\u0000 \u0000 4\u0000 4\u0000 \u0000\u0000-dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a \u0000\u0000 \u0000 4\u0000 4\u0000 \u0000\u0000-dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114405409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the essential norms of singular integral operators with constant coefficients and of the backward shift","authors":"Oleksiy Karlovych, E. Shargorodsky","doi":"10.1090/bproc/118","DOIUrl":"https://doi.org/10.1090/bproc/118","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be a rearrangement-invariant Banach function space on the unit circle <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper T\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">T</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {T}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H left-bracket upper X right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">H[X]</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be the abstract Hardy space built upon <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We prove that if the Cauchy singular integral operator <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper H f right-parenthesis left-parenthesis t right-parenthesis equals StartFraction 1 Over pi i EndFraction integral Underscript double-struck upper T Endscripts StartFraction f left-parenthesis tau right-parenthesis Over tau minus t EndFraction d tau\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mfrac>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mrow>\u0000 <mml:mi>π<!-- π --></mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mfrac>\u0000 <mml:msub>\u0000 <mml:mo>∫<!-- ∫ --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">T</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mfrac>\u0000 <mml:mrow>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>τ<!-- τ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mrow>\u0000 <mml:mi>τ<!-- τ --></mml:mi>\u0000 <mml:mo>−<!-- − -->","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132619762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adams-type maps are not stable under composition","authors":"Robert Burklund, Ishan Levy, Piotr Pstrkagowski","doi":"10.1090/bproc/137","DOIUrl":"https://doi.org/10.1090/bproc/137","url":null,"abstract":"<p>We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map to an <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper E Subscript normal infinity\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">E</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {E}_{infty }</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-<inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-algebra is a transfinite composition of Adams-type maps.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115036646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}